Nuclear Reactor Thermal Hydraulics-An Introduction to Nuclear Heat Transfer and Fluid Flow

1391 Pages·2019·145.429 MB·\1391

by  Robert E. Masterson (Author)

Common Parameters in Nuclear Science and Engineering

1 Watt (W) 1 joule per second
1 kilo Watt (KW) 1000 joules per second
1 mega Watt (MW) 1,000,000 joules per second

6.2 x 1012 MeV/sec 1 Joule/sec = 1 Watt
1 kilowatt hour (KwH) 3.6 x 106 joules

Relationship between Number of Fissions per Second and Thermal Energy Production

1 Watt Thermal Energy = 1 Joule/sec (Thermal) = 3.12 x 1010 fissions/second
Energy conversion using E = mc2: 1 AMU of mass m = 931.494 MeV/c2

Acceleration of Gravity and Time

Standard acceleration g 9.80665 m/s2 = 32.174 ft/s2
1 day 86,400 seconds
1 year 3.156 x 107 seconds

Units of Pressure

Metric pressures 1 Pascal = 1 Pa = 1 N/m2
Atmospheric pressure 1 atm = 14.696 PSI = 101.325 kPa = 1.01325 bar

Surface Tension, Specific Heat, and Specific Volume

Density 1 gm/cm3 = 1 kg/L = 1000 kg/m3 = 62.428 lb/ft3
Specific heat 1 kJ/kg - °C = 1 J/g - °C = 0.23885 BTU/lb- °F
Surface tension 1/N/m = 1000 dynes/cm = 0.0685 lb/ft
Specific volume 1 m3/kg = 1000 cm3/g = 16.02 ft3/lb
Physical volume 1 m3 = 1000 liters = 1 x 106 cm3 = 35.315 ft3 = 264.17 gallons (U.S.)

Stefan-Boltzmann Constant

s = 5.6704 x 10-8 W/m2 – K4

Heat of Vaporization of Water

h lv = 2257.1 kJ/kg = 970.4 BTU/lb (at atmospheric pressure)

Thermal Conductivity and Resistance

Thermal conductivity 1 W/m -°C = 0.5778 BTU/hr-ft-°F
Thermal resistance 1 °C/W = 0.5275 °F/hr-BTU

Viscosity

Dynamic viscosity 1 kg/m-s = 1 N–s/m2 = 2419.1 lb/ft-hr
Kinematic viscosity 1 m2/s = 104 stoke = 10.764 ft2/s
Nuclear Reactor Thermal Hydraulics
An Introduction to Nuclear Heat Transfer
and Fluid Flow

Nuclear Reactor Thermal Hydraulics
An Introduction to Nuclear Heat Transfer
and Fluid Flow
by
Robert E. Masterson, PhD (ScD in Nuclear Science and Engineering)
Massachusetts Institute of Technology
Cambridge, Massachusetts
CRC Press
Taylor & Francis Group
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Boca Raton, FL 33487-2742
© 2020 by Taylor & Francis Group, LLC
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Library of Congress Cataloging‑in‑Publication Data
Names: Masterson, Robert, 1950- author.
Title: Nuclear reactor thermal hydraulics / Robert Masterson.
Description: Boca Raton : CRC Press, [2019]
Identifiers: LCCN 2018058907 | ISBN 9781138035379 (hardback : alk. paper) |
ISBN 9781315226231 (ebook)
Subjects: LCSH: Nuclear reactors—Cooling. | Nuclear
reactors—Thermodynamics. | Nuclear reactors—Fluid dynamics. | Thermal
hydraulics.
Classification: LCC TK9212 .M378 2019 | DDC 621.48/35—dc23
LC record available at https://lccn.loc.gov/2018058907
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eResource material is available for this title at
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Contents
Preface xxv CHAPTER 2
An Overview of the Book xxvii
The Pressurized Water Reactor 37
Author xxxiii
2.1 Pressurized Water Reactors 37
2.2 PWR Cores and Pressure Vessels 37
CHAPTER 1
2.3 Core Design Parameters 39
Nuclear Power in the World Today 1 2.4 Flow Paths through the Pressure
Vessel and the Core 39
1.1 Types of Reactors and Their Characteristics 1
2.5 Steam Generators 40
1.2 Number of Power Reactors around the World 1
2.6 Steam Generator Characteristics
1.3 Power Reactor Architectures 4
and Their Internal Geometries 42
1.4 Power Reactors and Their Design Features 6
2.7 Reactor Coolant Pumps 43
1.5 Schematic of a Nuclear Power Plant 6
2.8 The Pressurizer 45
1.6 Coolants Used in Nuclear Power Plants 8
2.9 Fuel Assemblies for PWRs 47
1.7 Types of Nuclear Fuel 10
2.10 VVER Reactors and Russian PWRs 49
1.8 Properties of Nuclear Fuel 12
2.11 Canadian Pressurized Heavy Water
1.9 Reactor Pressure Vessels and Their Properties 13
Reactors (CANDU Reactors) 50
1.10 Characteristics of Reactor Cores 15
2.12 Fuel Assemblies for PHWRs
1.11 Characteristics of Reactor Fuel Assemblies 15
(CANDU Reactors) 52
1.12 Other Important Reactor Properties
2.13 Coolant Temperature Profiles in
(Power Density and Thermal Efficiency) 17
Different Reactor Designs 55
1.13 The Power Density 18
2.14 Temperature Profiles in a PWR Core 55
1.14 Thermal Efficiency 19
2.15 Movement to Standard Reactor Designs 56
1.15 Control Rods and Their Function 21
2.16 Advanced Reactor Concepts 57
1.16 Comparing PWR Control Rods
2.16.1 The Trend toward Passive
and BWR Control Rods 22
Safety Systems 57
1.17 Use of the Scram Button
2.16.2 The Westinghouse AP-1000 58
and the Word SCRAM 24
2.17 Characteristics of PWRs 58
1.18 Maintaining the Criticality
2.18 Core Characteristics and Design Parameters 59
of the Core over Time 25
2.19 Understanding How the Passive Cooling
1.19 Electrical Generating Systems
System Works in the Westinghouse AP-1000 60
in a Nuclear Power Plant 25
2.20 Boric Acid in PWRs 64
1.20 SGs and Their Uses 25
Bibliography 66
1.21 Steam Turbines 26
Books and Textbooks 66
1.22 SG and Steam Turbine Pairing 26
Web References 66
1.23 Electrical Generators in Nuclear Power Plants 27
Questions for the Student 66
1.24 Common Measurements of
Exercises for the Student 67
Electrical Power Production 29
1.25 Nikola Tesla and Thomas Edison
and Their Contributions to the CHAPTER 3
Field of Nuclear Power 30 The Boiling Water Reactor 69
1.26 The Relationship between Nikola
Tesla and George Westinghouse 32 3.1 Boiling Water Reactors 69
1.27 Reviewing What We Have Just Learned 33 3.2 Types of American BWRs 70
Bibliography 33 3.3 Fuel Assemblies for BWRs 72
Books and Textbooks 33 3.4 Power Control in a BWR 74
Web References 34 3.5 Russian BWRs (RBMKs) 74
Questions for the Student 34 3.5.1 RBMK Design Parameters 74
Exercises for the Student 35 3.6 Temperature Profiles in a Typical BWR Core 76
v
vi CONTENTS
3.7 The Advanced BWR and the Simplified BWR 78 5.2 Measuring Nuclear Energy 121
3.8 The Simplified BWR 79 5.3 Examining the Fission Process 122
3.9 Characteristics of BWRs 80 5.4 Cross Sections and Reaction Rates 122
3.10 Core Characteristics and Design Parameters 80 5.5 Converting the Kinetic Energy of
3.11 The Void Fraction and the Nuclear Particles into Thermal Energy 125
Quality in a BWR Core 81 5.6 Energy Produced by the Fission Process 126
3.12 Finding the Density from the Void Fraction 81 5.7 Estimating the Total Energy Release 127
3.13 The Relationship between the 5.8 Other Types of Nuclear
Void Fraction and the Quality 83 Particles and Radiation 128
3.14 BWR Flow Regimes 85 5.9 Gamma Rays and Their Properties 129
3.15 Operating Restrictions for a Typical BWR 88 5.10 Radioactive Decay Heat 129
3.16 BWR Operating Maps 88 5.11 Attenuation Coefficients for Different
3.17 Lessons That Can Be Learned Types of Nuclear Radiation 130
from a Reactor Operating Map 89 5.12 Energy of Fission Neutrons 131
Bibliography 91 5.13 The Maxwell–Boltzmann
Books and Textbooks 91 Probability Distribution 134
Web References 92 5.14 Thermal Energy Produced
Questions for the Student 92 in Nuclear Fuel Rods 135
Exercises for the Student 93 5.15 The Fuel Rod Cladding 137
5.16 Nuclear Fuel Assemblies 139
5.17 PWR, BWR, and LMFBR Fuel Assemblies 139
CHAPTER 4
5.18 The Number of Fuel Rods in a Fuel Assembly 141
Fast Reactors, Gas Reactors, and Military Reactors 95 5.19 Fuel Rods in Square Fuel Assemblies 141
5.20 Fuel Rods in Hexagonal Fuel Assemblies 141
4.1 An Introduction to Other Reactor Types 95
5.21 CANDU Reactor Fuel Assemblies 143
4.2 Advantages of Fast Reactors 95
5.22 Where Nuclear Energy Is
4.3 Fast Reactor Coolants 95
Produced in the Core 144
4.4 Advanced Gas Reactors 96
5.23 Ways of Measuring the Core Power 145
4.5 Liquid Metal Fast Breeder Reactors 97
5.24 Heat Generation in Nuclear Fuel Assemblies 147
4.6 Fuel Assemblies for LMFBRs 99
5.25 The Volumetric Power Densities
4.7 Temperature Profiles in an LMFBR Core 102
for Different Reactor Types 149
4.8 Other Reactor Concepts 102
5.26 Power Densities in Reactor Fuel Assemblies 150
4.9 Military Reactors and the MPR 104
5.27 Power Profiles in Reactor Fuel Assemblies 150
4.10 High-Temperature Gas Reactors 106
5.28 Using Burnable Poisons to Flatten the
4.11 HTGR Fuel 106
Power and Temperature Profile 152
4.12 Comparing the Designs of Gas Reactors 107
5.29 Axial Power Shapes and Power Peaks 153
4.13 Gas Reactor Cores and Design Parameters 110
5.30 Using Axial Zoning to Reduce Power Peaks 154
4.14 LMFBR Thermal Cycle Performance 111
5.31 Finding the Power Profiles in Simple Reactors 155
4.15 Characteristics of LMFBR Cores 112
5.32 Neutron Reflectors 155
4.16 Comparing the Power Densities
5.33 Axial Power Profiles in Uniform,
in Different Reactor Cores 113
Unreflected Cores 156
4.17 The NSSS and the Containment
5.34 Radial Power Profiles in
Building for Fast Reactors 114
Uniform, Unreflected Cores 157
4.18 Theoretical Thermal Efficiencies 115
5.35 Cylindrical Power Profiles
4.19 Earliest Fast Reactors 116
and Bessel Functions 158
Bibliography 117
5.36 Extrapolated Power Profiles 158
Books and Textbooks 117
5.37 Global Power Profiles in
Web References 117
Different Types of Cores 161
Questions for the Student 117
5.38 Core Peak-to-Average Power Ratios
Exercises for the Student 119
for Uniform, Unreflected Cores 162
5.39 Power Profiles for Heterogeneous Cores 162
CHAPTER 5 5.40 Flattening the Power Profile 162
5.41 How Control Rods Affect the
Thermal Energy Production in Nuclear Power Plants 121
Core-Wide Power Profile 163
5.1 Heat Production in Nuclear Power Plants 121 5.42 Power Fluctuations in Steady-State Cores 165
CONTENTS vii
5.43 Where Thermal Energy Is 6.24 Fluidic Work 198
Deposited in the Core 167 6.25 The Definition of Power 198
5.44 Sources of Decay Heat 167 6.26 The Definition of Pressure 199
5.45 Fission Products and Actinides 167 6.27 The Units of Pressure 199
5.46 Decay Heat from Beta Decay 167 6.28 Thermodynamic Cycles and Path Functions 201
5.47 Cherenkov Radiation 168 6.29 Using Thermodynamic State Variables 201
5.48 Decay Heat as a Function of Burnup 169 6.30 Understanding the Internal
5.49 Removing Decay Heat from the Core 169 Energy and the Enthalpy 202
5.50 Decay Heat Removal after Shutdown 171 6.31 Finding the Enthalpy When a
5.51 ANS Standards Governing Decay Heat 173 Material Changes Phase 203
Bibliography 174 6.32 Adding Heat to a Two-Phase Mixture 207
Books and Textbooks 174 6.33 The Temperature Behavior of Single-
Web References 174 Phase Flows and Two-Phase Mixtures 207
Questions for the Student 175 6.34 The Saturation Temperature and
Exercises for the Student 177 the Saturation Pressure 209
6.35 The Clausius–Clapeyron Equation 209
6.36 The Relationship between the
CHAPTER 6
Pressure and the Boiling Point of
The Laws of Thermodynamics 179 Water in Light Water Reactors 210
6.37 Relationships between Common
6.1 An Introduction to the Laws
Thermodynamic Variables 211
of Thermodynamics 179
6.38 Pressure–Temperature Diagrams
6.2 The First Law of Thermodynamics 179
and Phase Diagrams 211
6.3 Understanding Energy Transfer
6.39 Temperature–Volume Diagrams 213
in Nuclear Systems 181
6.40 Pressure–Volume Diagrams 214
6.4 Forms of Nuclear Energy Transfer 182
6.41 Heat Engines 214
6.4.1 Heat Energy Leading
6.42 The Carnot Thermal Cycle 215
to Heat Transfer 182
6.43 Thermal Efficiencies of Nuclear Power Plants 216
6.4.2 Heat Transfer 182
Bibliography 217
6.4.3 Mass Transfer 183
Books and Textbooks 217
6.4.4 Work Transfer 183
Questions for the Student 218
6.5 Generalized Energy Transfer 183
Exercises for the Student 219
6.6 Heat Energy and the First Law
of Thermodynamics 184
6.7 Thermal Efficiency and the First Law 185 CHAPTER 7
6.8 The Second Law of Thermodynamics 185
Thermodynamic Properties and Equations of State 221
6.9 Alternative Statements of the Second Law 186
6.10 The Clausius Inequality 187 7.1 Thermodynamic Properties
6.11 The Increase in Entropy Principle 188 and Nuclear Power Plants 221
6.12 The Third Law of Thermodynamics 189 7.2 Comparisons to Coal-Fired Power Plants 222
6.13 The Fourth or the Zeroth Law 7.3 Thermodynamic State Variables 222
of Thermodynamics 190 7.4 Thermodynamic Equations of State 222
6.14 Understanding the Difference between 7.5 The Equation of State for the Ideal Gas Law 223
Thermodynamics and Heat Transfer 191 7.6 Treating Steam as an Ideal Gas 224
6.15 Other Comparisons between 7.7 Measuring the Deviation of
Thermodynamics and Heat Transfer 192 Steam from an Ideal Gas 225
6.16 Thermodynamic Properties, 7.8 Other Equations of State 225
Systems, and States 192 7.9 Inferring the Behavior of Reactor
6.17 Defining a Pure Material or Substance 192 Coolants from Other State Variables 226
6.18 The Thermodynamic State of a Material 193 7.10 Defining the Enthalpy and
6.19 The Temperature of a Material 193 Specific Enthalpy of a Fluid 227
6.20 Nuclear Temperature Scales 193 7.11 Finding the Enthalpy of a
6.21 The Definition of Heat 195 Two-Phase Mixture 228
6.22 The Definition of Energy 195 7.12 Phase Changes in Reactor Coolants 229
6.23 The Definition of Work 197 7.13 Property Diagrams 230
viii CONTENTS
7.14 Using Property Diagrams to Books and Textbooks 264
Describe Phase Changes 230 Web References 265
7.15 Pressure–Temperature Diagrams 232 Questions for the Student 265
7.16 Temperature–Volume Diagrams 232 Exercises for the Student 266
7.17 Pressure–Volume Diagrams 233
7.18 Defining the Saturation
CHAPTER 8
Temperature and Pressure 234
7.19 The Clausius–Clapeyron Equation 234 The Nuclear Steam Supply System and Reactor
7.20 Determining the Boiling Point from Heat Exchangers 269
Clausius–Clapeyron Equation 234
8.1 The Nuclear Steam Supply System 269
7.21 Properties of Liquid–Vapor Mixtures 235
8.2 Understanding the NSSS 270
7.22 The Quality of a Two-Phase Mixture 235
8.3 The Components of the NSSS 272
7.23 Using the Quality to Define the
8.4 Thermal Efficiency Optimization 274
Properties of a Two-Phase Mixture 236
8.5 Reactor Coolant Pumps 275
7.24 Relationships between the Quality
8.6 Reactor Steam Generators 275
and the Void Fraction 237
8.7 Types of Reactor SGs 277
7.25 Finding the Entropy of a Two-Phase Mixture 239
8.8 SG Design Parameters 279
7.26 The Steam Tables 239
8.9 More on Reactor SGs 279
7.27 Thermodynamic Properties
8.10 SGs and Heat Exchangers 281
of Water and Steam 240
8.11 Steam Turbines 282
7.28 The Behavior of Air–Water Mixtures 245
8.12 Multistage Steam Turbines 283
7.29 Using the Steam Tables to Determine
8.13 SG and Steam Turbine Pairings 283
the Properties of Pressurized Water 247
8.14 Electrical Generators 284
7.30 Using the Steam Tables to
8.15 How an Electric Generator Works 284
Calculate the Enthalpy 247
8.16 Condensers and Other Heat Rejection Devices 287
7.31 Thermodynamic Cycles and Path Functions 247
8.17 The Demineralizer 288
7.32 The Relationship between the Path a System
8.18 Feedwater Heaters 289
Takes, and Its Heat and Work Output 249
8.19 Types of Reactor Cooling Towers 289
7.33 Deriving Work from a State Diagram 250
8.20 Heat Transfer through a
7.34 Finding the Thermal Efficiency
Reactor Cooling Tower 291
from a T–S Diagram 251
8.21 Types of Heat Exchangers 293
7.35 Defining the Energy Storage
8.22 Heat Exchanger Design 295
Capacity of a Material 254
8.23 Finding the Heat Transfer Rate
7.36 Definitions of the Specific Heats 254
through a Heat Exchanger Tube 297
7.37 Specific Heat at Constant Volume 255
8.24 Exploring the Log-Mean
7.38 Specific Heat at Constant Pressure 255
Temperature Difference 300
7.39 The Specific Heat for a Pure Substance 255
8.25 Assumptions Regarding the LMTD 300
7.40 The Specific Heat for an Ideal Gas 257
8.26 Comparing the Virtues of Parallel-Flow
7.41 Other Ways to Find the Specific Heat 258
and Counterflow Heat Exchangers 302
7.42 Tabulated Values for the Specific Heat 260
8.27 Practical Applications of the LMTD 302
7.43 Applying the Specific Heats to Solids
8.28 Heat Flows in Cross-Flow Heat Exchangers 304
and Incompressible Liquids 260
8.29 Accounting for Crud Buildup
7.44 Applying Specific Heats to
in Heat Exchanger Tubes 304
Reactor Coolant Pumps 260
8.30 Tube Fouling Factors 305
7.45 Calculating the Heat Transfer
8.31 Tube Vibration in Reactor SGs 307
Rate Using the Specific Heats 261
8.32 Fluid Properties and Their Effect
7.46 Determining the Coolant
on Thermal Efficiency 307
Temperature Profiles in a PWR 262
Bibliography 309
7.47 Performing an Energy Balance Using the
Books and Textbooks 309
Enthalpy in a Reactor Heat Exchanger 263
Web References 310
7.48 More Accurate Methods for Finding the
Other Reference 310
Boiling Point of a Reactor Coolant 264
Questions for the Student 310
Bibliography 264
Exercises for the Student 311